dirty vertex color with the multiresolution
Not currently. I know of one person who has been on a campaign over this issue for a long time now.
I always have UV's built early so what I do is duplicate the object then move it to another layer.  Then I apply the modifier and bake the results to a texture.   

Then I delete the duplicated object and apply the baked texture to the original model which still has the modifier.

Once you get used to doing this it can be usually be redone within a couple of minutes so you can redo it easily if you have updated the mesh and require a rebake.

Here are the relevant bake settings that I use. 



BTW, even though there is a bake pass type called Vertex Colors, it does not produce the results that I expect.  For me it always bakes much darken than it should but maybe I'm doing something wrong.  The settings I showed here work well.